I linked to this in this RPGnet thread about, yes, Doctor Who Christmas Special ideas. Lots of possibilities (check out the list of events occurring in late December throughout history) and I threw in two of my own.
The Green Knight
Landing in London, Christmas 1540, the travellers detect that someone is using anachronistic technology to affect the weather, making it snow severely as Henry the Eighth holds his winter court, keeping him inside.
"I don't think they're here about the dissolution of the monasteries..."
They overshot a time-travelling attempt to wipe out the 21st Century space program and protect Mars, and are now trying to wreck English efforts to found colonies in the Americas to stop that happening.
And another one, going the other way:
Following Yonder Star
We open on a group of children under a Christmas tree, being told they can open one present now then it's off to bed. And we pan up and back to their window... and a field of stars streaking past.
The year 2091. A united Earth spaceship, heading for the first terraformed colony on another world. Six months into a twelve-year flight. Christmas among the stars.
And someone wants to stop the mission. Dead.